How to create a gradient colour like on the picture and the apply it on a mesh
You may achieve it using the Gradient Texture and Color Ramp nodes. 


Set up the material nodes as pictured below.


You may also add a Mapping Node to change the location, rotation or scale of a gradient.


Try to change the Gradient Texture's type to for example Radial, Diagonal or Quadratic Sphere and experiment with a Mapping node and Color Ramp settings for different results.




You may also add a Bright/Contrast node between Color Ramp and Diffuse nodes to make some quick color adjustments.

Here's a .blend file with the closest effect to the reference you provided: